A141812
RMS values of the RMS numbers: a(n) is the root mean square of the divisors of A140480(n).
Original entry on oeis.org
1, 5, 29, 169, 145, 845, 1105, 2405, 3445, 4901, 2665, 5525, 9425, 12325, 12025, 17225, 24505, 13325, 32045, 55205, 47125, 61625, 69745, 101065, 99905, 77285, 124501, 160225, 186745, 204425, 239425, 160225, 273325, 276025, 292825, 226525, 446165, 456025
Offset: 1
a(5)=145, because A140480(5)=287, with divisors 1,7,41,287 and RMS(1,7,41,287) = 145.
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rmsQ[n_] := IntegerQ[Sqrt[DivisorSigma[2, n]/DivisorSigma[0, n]]]; Reap[ For[k=1; n=1, k<10^7, k++, If[rmsQ[k], an = Sqrt[Mean[Divisors[k]^2]]; Print["k = ", k, " a(", n++, ") = ", an]; Sow[an]]]][[2, 1]] (* Jean-François Alcover, Dec 04 2015 *)
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for(n=1,1e6,if(issquare(sumdiv(n,d,d^2)/numdiv(n),&s) && denominator(s)==1,print1(s", "))) \\ Charles R Greathouse IV, Mar 08 2013
A141813
Primitive RMS numbers: RMS numbers which are not the product of two smaller RMS numbers.
Original entry on oeis.org
1, 7, 41, 239, 3055, 6665, 9545, 9855, 26095, 34697, 155287, 380511, 421655, 627215, 814463, 823537, 1166399, 1204281, 1256489, 1289441, 1815073, 2265353, 2544697, 2627343, 3132935, 3188809, 3762639, 4647985, 4730879, 4963127, 4995569, 5054015, 5143945
Offset: 1
The RMS Number 287 is not in the sequence because 287=7*41 and both 7 and 41 are RMS numbers.
A141815
RMS numbers with non-unique RMS values.
Original entry on oeis.org
627215, 876785, 1289441, 1815073, 2265353, 3132935, 3188809, 4390505, 4647985, 4730879, 6542705, 9026087, 11369969, 12705511, 15203889, 15857471, 17888153, 18253913, 18578719, 20871649, 21026655, 21930545, 22321663, 23630711
Offset: 1
627215 is an RMS Number with an RMS value of 160225.
876785 is an RMS Number with an RMS value of 160225.
Since these two RMS numbers have the same RMS value, their RMS values are non-unique and therefore they belong to the sequence.
A141816
RMS values of the RMS numbers with non-unique RMS values: a(n) is the Root Mean Square of the divisors of A141815(n).
Original entry on oeis.org
160225, 160225, 456025, 456025, 801125, 801125, 801125, 801125, 1185665, 1185665, 1185665, 2280125, 4032145, 2280125, 4032145, 4005625, 6326125, 6456125, 6569225, 5226065, 4032145, 4005625, 4005625, 5928325, 6326125
Offset: 1
a(1)=160225, because A141815(1)=627215 and the Root Mean Square of the divisors of 627215 is 160225.
Showing 1-4 of 4 results.
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